Cyberworlds are being formed in cyberspaces as computational spaces. Now cyberspaces are rapidly expanding on the Web either intentionally or spontaneously, with or without design. Widespread and intensive local activities are melting each other on the web globally to create cyberworlds. The major key players of cyberworlds include e-finance that trades a GDP-equivalent a day and e-manufacturing that is transforming industrial production into Web shopping of product components and assembly factories. Lacking proper theory and design, cyberworlds have continued to grow chaotic and are now out of human understanding and control. This research first presents a generic theoretical framework and design based on algebraic topology, and also provides an axiomatic approach to theorize the potentials of cyberworlds.